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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6320 • Algebra II

Fall 2024 • Question 4

Question

Math 6320 • Algebra II Fall 2024 • Question 4

Show that if \(L/K\) is Galois and \(f \in K[x]\) is monic irreducible, then every irreducible factor of \(f\) in \(L[x]\) has the same degree.

Raw LaTeX

Show that if \(L/K\) is Galois and \(f \in K[x]\) is monic irreducible, then every
irreducible factor of \(f\) in \(L[x]\) has the same degree.

Topic Tags

Galois Theory Irreducible Polynomials